The Potion Riddle
by AnnekeRose
Summary: Examining the Potion's Riddle and the logic behind solving it.


Format your text to a FIX WIDTH FONT (such as: Courier) To see it properly  
  
The potions are a logic puzzle. On a roll of paper next to the potions is this riddle:   
  
Danger lies before you, while safety lies behind,   
Two of us will help you, which ever you would find,   
One among us seven will let you move ahead,   
Helful Forward = HF  
  
Another will transport the drinker back instead,   
Helful Back = HB  
  
Two among our number hold only nettle wine,   
Nettle Wine = NW  
  
Three of us are killers, waiting bidden in line.   
Killers = K  
  
Choose, unless you wish to stay here forevermore,   
To help you in your choice, we give you these clues four:   
  
First, however slyly the poison tries to hide   
You will always find some on nettle wine's left side:   
  
1 2 3 4 5 6 7  
ANW K NW K   
BNW K NW K   
CNW K NW K   
DNW K NW K   
E NW K NW K   
F NW K NW K   
G NW K NW K   
H NW K NW K   
I NW K NW K   
K NW K NW K   
  
  
Ofcourse the above shows it on NW's left side (as if it was a person looking at you). What if the puzzle simply meant on the left side of NW, which is more likely what the author ment. This is taking in  
  
1 2 3 4 5 6 7  
#A K NW K NW  
#B K NW K NW  
#C K NW K NW  
#D K NW K NW  
#E K NW K NW  
#F K NW K NW  
#G K NW K NW  
#H K NW K NW   
#I K NW K NW  
#K K NW K NW  
Second, different are those who stand at either end,   
But if you would move onward, neither is your friend;   
So position 1 & 7 must be different and either: NW, K, or HB.  
  
1 2 3 4 5 6 7  
ANW K NW K K  
A2NW K NW K HB  
BNW K NW K K  
B2NW K NW K HB  
CNW K NW K K  
C2NW K NW K HB  
DNW K NW K   
EK NW K NW K HFHB  
E2HB NW K NW K HFK  
FK NW K HF NW K HB  
F2HB NW K HF NW K K  
GHB NW K NW K   
G2K NW K NW HB   
HK HF NW K NW K HB  
H2HB HF NW K NW K K  
IHB ? NW K ? NW K   
I2K ? NW K ? NW HB   
K HB NW K NW K  
1 2 3 4 5 6 7  
#A K NW K NW HB  
#B K NW K NW HB  
#C K NW K NW HB  
#D K NW K NW  
#E K K NW K NW HB  
#E2 HB K NW K NW K  
#F K K NW K NW HB  
#F2 HB K NW K NW K  
#G K K NW K NW  
#G2 HB K NW K NW  
#H K K NW K NW HB   
#H2 HB K NW K NW K   
#I K K NW K NW  
#I2 HB K NW K NW  
#K K K NW K NW  
#K2 HB K NW K NW  
Third, as you see clearly, all are different size,   
Neither dwarf nor giant holds death in their insides;   
  
We have to skip this one, because we don't know what sizes the bottles are.  
Fourth, the second left and the second on the right   
Are twins once you taste them, though different at first sight.  
So 2 and 6 must be the same. So they can't be HB or HF.  
  
1 2 3 4 5 6 7  
ANW K NW K K- Can't be (All K's layed out)  
A2NW K NW K HF K HB  
BNW K HF NW K K K- Can't be (All K's layed out)  
B2NW K HF NW K K HB  
CNW K NW K K  
C2NW K NW K HB  
DNW K NW K - Can't be (All NW layed out)   
EK NW K NW K HFHB- Can't be (NW & HF are different)  
E2HB NW K NW K HFK- Can't be (NW & HF are different)  
FK NW K HF NW K HB- Can't be (NW & K are different)  
F2HB NW K HF NW K K- Can't be (NW & K are different)  
GHB NW K NW K   
G2K NW K NW HB   
HK HF NW K NW K HB- Can't be (HF & K are different)  
H2HB HF NW K NW K K- Can't be (HF & K are different)  
IHB NW K NW K - Can't be (All NW layed out)  
I2K NW K NW HB - Can't be (All NW layed out)  
K HB NW K NW K- Can't be (All NW layed out)  
1 2 3 4 5 6 7  
#A K NW K NW HB- Can't be (All NW layed out)  
#B K NW K NW HB- Can't be (All NW layed out)  
#C K NW K NW HB  
#D K NW K NW- Can't be (NW & K are different)  
#E K K NW K NW HB- Can't be (All K layed out)  
#E2 HB K NW K NW K- Can't be (All K layed out)  
#F K K NW K NW HB- Can't be (NW & K are different)  
#F2 HB K NW K NW K- Can't be (NW & K are different)  
#G K K NW K NW  
#G2 HB K NW K NW  
#H K K NW K NW HB - Can't be (All NW layed out)  
#H2 HB K NW K NW K - Can't be (All NW layed out)  
#I K K NW K NW- Can't be (All K layed out)  
#I2 HB K NW K NW- Can't be (All K layed out)  
#K K K NW K NW- Can't be (All K layed out)  
#K2 HB K NW K NW- Can't be (All K layed out)  
That indicates that of the seven bottles, three are poison, two are wine, one will get a person safely through the black fire, and one will get a person back through the purple.   
  
Solutions LEFT  
1 2 3 4 5 6 7  
A2NW K NW K HF K HB  
BNW K HF NW K K K  
B2NW K HF NW K K HB  
CNW K HF HB NW K K  
C2NW K HF K NW K HB  
C3NW K HB HF NW K K  
C4NW K K HF NW K HB  
GHB NW K HF K NW K   
G2K NW K HF K NW HB   
G3HB NW K K HF NW K   
G4K NW K K HF NW HB   
1 2 3 4 5 6 7  
#C K NW K HF K NW HB  
#C2 K NW HF K K NW HB  
#G K K NW HF HB K NW  
#G2 HB K NW HF K K NW  
#G3 K K NW HB HF K NW  
#G4 HB K NW K HF K NW  
#K2 HB HF K K NW K NW  
#K2 HB K HF K NW K NW  
This puzzle is particularly ingenious because many very clever wizards have no sense of logic at all, which would mean that they would be stuck in that chamber, unable to go forward or back.   
  
The solution is this:   
  
The potion in the smallest bottle will get a person through the black flame and on to the Chamber of the Stone. The potion in the rounded bottle at the right end of the line will provide safe passage back through the purple flames.   
  
Solutions LEFT  
1 2 3 4 5 6 7  
A2NW K NW K HF K HB  
BNW K HF NW K K K - Can't Be (Not on the Right side).  
B2NW K HF NW K K HB  
CNW K HF HB NW K K - Can't Be (Not on the Right side).  
C2NW K HF K NW K HB  
C3NW K HB HF NW K K - Can't Be (Not on the Right side).  
C4NW K K HF NW K HB  
GHB NW K HF K NW K - Can't Be (Not on the Right side).   
G2K NW K HF K NW HB   
G3HB NW K K HF NW K - Can't Be (Not on the Right side).   
G4K NW K K HF NW HB   
  
1 2 3 4 5 6 7  
#C K NW K HF K NW HB  
#C2 K NW HF K K NW HB  
#G K K NW HF HB K NW- Can't Be (Not on the Right side).  
#G2 HB K NW HF K K NW- Can't Be (Not on the Right side).  
#G3 K K NW HB HF K NW- Can't Be (Not on the Right side).  
#G4 HB K NW K HF K NW- Can't Be (Not on the Right side).  
#K2 HB HF K K NW K NW- Can't Be (Not on the Right side).  
#K2 HB K HF K NW K NW- Can't Be (Not on the Right side).  
Still leaves us with:  
Solutions LEFT  
1 2 3 4 5 6 7  
A2NW K NW K HF K HB  
B2NW K HF NW K K HB  
C2NW K HF K NW K HB  
C4NW K K HF NW K HB   
G2K NW K HF K NW HB   
G4K NW K K HF NW HB   
  
1 2 3 4 5 6 7  
#C K NW K HF K NW HB  
#C2 K NW HF K K NW HB  
We know that 1 & 7 must be different and not helpful so HF is not in either of those two positions. We also know that 2 & 6 are the same and since there is only one bottle of HF it can't be there either. So we know that the HF potion must be somewhere in the middle.  
  
Hermonie may have gone about the following way to the solution.  
  
She knew 2 & 6 had to be either NW or the Killer.  
  
1 2 3 4 5 6 7  
A NW NW  
B K K  
  
She knew 1 & 7 had to be different but not helpful to move forward.  
Since the NW are layed out 1 & 7 have to be Killer and Helful back  
1 2 3 4 5 6 7  
A K NW NW HB  
  
Now for the second choice she knew it could be K, NW, or HB in either 1 or 7  
1 2 3 4 5 6 7  
B K K K NW  
B2 K K K HB  
B3 NW K K HB  
  
Using that the Killer would always be on NW left side:  
  
1 2 3 4 5 6 7  
A K NW K NW HB  
  
1 2 3 4 5 6 7  
B K K NW K NW  
  
The following two, you can't put the 2 NW down and have K on it's left.  
B2 K K K HB   
B3 NW K K HB  
So we are left with two solutions. We know the outcome was that HB was on the far Right side, so that leaves us with only:  
  
1 2 3 4 5 6 7  
A K NW K NW HB  
  
So how did Hermonie know which bottle was the correct one? She only had K and the HF left to place. Obviouslly 3 or 4 was a drawf or the smallest bottle. Knowing it doesn't have death inside it, she knew it had to be the HF potion.  
  
However, I still wish the author gave us the descriptions of the bottles so we could figure it out by our selves, as I like logic puzzles like this. :( 


End file.
